The present invention relates to a method of and a system for carrying out an approximation process for circuit analysis of a distributed constant line. In particular, the present invention relates to a method and a system for approximating a distributed constant line by a lumped constant circuit, with specified accuracy. The present invention also relates to a storage medium that stores a program used therefor.
With regard to a wiring system such as a printed board or a multilayer wiring board, it is required to carry out circuit analysis concerning whether the circuit realizes desired operation. Conventionally, analysis software has been developed for this object. By designating circuit elements constituting a circuit, a circuit model is specified, and then, the above-mentioned software is used for circuit analysis on a computer.
As LSIs are rapidly improved in their operating speed, a wiring system for transmitting signal between elements is required to have structure capable of transmitting a signal at high speed. To that end, it is necessary to sufficiently understand signal transmission characteristics of a wiring system. In that case, in order to realize high speed transmission, a wiring system should be treated as a transmission line so that its transmission characteristics can be understood accurately.
However, a circuit to be analyzed includes, in addition to transmission lines, circuit elements that should be treated as lumped constants. Thus, lumped constant and distributed constant coexist. However, circuit analysis of a lumped constant/distributed constant mixed system is difficult, since a travelling wave of voltage/current should be treated.
Thus, it is demanded to approximate a distributed constant line by a lumped constant circuit. In the approximation, it is desirable that the degree of accuracy of the approximation be known. Further, when the approximation accuracy becomes higher, a load on the processing becomes larger. Thus, in approximating a distributed constant line by a lumped constant circuit, it is desired that the approximation can be carried out with a required accuracy.
An object of the invention is to provide a process for approximating a distributed constant line by a lumped constant circuit, and, in particular, to provide a method and system for approximating a distributed constant line with a required accuracy, and a storage medium that stores a program used therefor.
To attain the above object, the present invention provides, according to its first mode, a method of approximating a distributed constant line, which employs an information processing apparatus to perform a process of approximating an object distributed constant line by a lumped constant circuit obtained by cascading a given unit lumped constant circuit in n stages, comprising the steps of:
calculating a product xcex3l of a propagation constant xcex3 of the object distributed constant line and a line length l of the distributed constant line, and storing the product;
calculating cosh xcex3l and sinh xcex3l, using the xcex3l, and storing the cosh xcex3l and sinh xcex3l;
calculating an(xcex3l), bn(xcex3l) and cn(xcex3l) that constitute elements of a transfer matrix of the lumped constant line, from functions an(x), bn(x) and cn(x) defined by following three expressions:                     a        n            ⁢              (        x        )              =                  ∑                  k          =          0                n            ⁢                                                                  (                                  n                  +                  k                  -                  1                                )                            !                        ⁢                          xe2x80x83                                                                          n                                                      2                    ⁢                    k                                    -                  1                                            ⁢                              (                                  n                  -                  k                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                          2              ⁢              k                                                          (                              2                ⁢                k                            )                        !                                                  b        n            ⁢              (        x        )              =                  ∑                  k          =          0                          n          -          1                    ⁢                                                  (                              n                +                k                            )                        !                                                              n                                                      2                    ⁢                    k                                    +                  1                                            ⁢                              (                                  n                  -                  k                  -                  1                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                                          2                ⁢                k                            +              1                                                          (                                                2                  ⁢                  k                                +                1                            )                        !                                                  c        n            ⁢              (        x        )              =                  ∑                  k          =          0                n            ⁢                                                  (                                                n                  2                                +                                  k                  2                                            )                        ⁢                                          (                                  n                  +                  k                  -                  1                                )                            !                                                                          n                                                      2                    ⁢                    k                                    +                  1                                            ⁢                              (                                  n                  -                  k                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                                          2                ⁢                k                            +              1                                                          (                                                2                  ⁢                  k                                +                1                            )                        !                              
xe2x80x83putting x=xcex3l and deciding n as a tentative value, and storing the an(xcex3l), bn(xcex3l) and cn(xcex3l);
comparing the cosh xcex3l with an(xcex3l), sinh xcex3l with bn(xcex3l), and sinh xcex3l with cn(xcex3l), respectively, to make a judgment on whether a result of comparison satisfies a predetermined condition, and, when the condition is not satisfied, repeating steps from the step of calculating the an(xcex3l), bn(xcex3l) and cn(xcex3l), onward, changing the value of the n, until the result of comparison satisfies the condition; and
deciding an approximate circuit, using n when the result of comparison satisfies the condition, in order to decide a lumped constant circuit that is obtained by cascading the unit lumped constant circuit in n stages.
In the above-described method, further, the following modes may be optionally employed.
a) The above-mentioned comparison is carried out by calculating a deviation between the cosh xcex3l and an(xcex3l), a deviation between sinh xcex3l and bn(xcex3l), and a deviation between sinh xcex3l and cn(xcex3l), respectively, and the result of comparison is obtained as the maximum xcex4 among those deviations; and
a condition that the maximum xcex4 satisfies xcex4 less than xcex5 for an error tolerance xcex5 set in advance is used as the condition to make the judgment.
b) The above-mentioned lumped constant circuit is constituted by cascading a Π circuit as the unit lumped constant circuit in n stages, and the transfer matrix of the lumped constant circuit is given by an expression:       F    Π    =      [                                                      a              n                        ⁡                          (                              γ                ⁢                                  xe2x80x83                                ⁢                l                            )                                                                          Z              0                        ⁢                                          b                n                            ⁡                              (                                  γ                  ⁢                                      xe2x80x83                                    ⁢                  l                                )                                                                                                    1                              Z                0                                      ⁢                          xe2x80x83                        ⁢                                          c                n                            ⁡                              (                                  γ                  ⁢                                      xe2x80x83                                    ⁢                  l                                )                                                                                        a              n                        ⁡                          (                              γ                ⁢                                  xe2x80x83                                ⁢                l                            )                                            ]  
xe2x80x83where Z0 is a characteristic impedance of the distributed constant line.
c) The above-mentioned lumped constant circuit is constituted by cascading a T circuit as the unit lumped constant circuit in n stages, and the transfer matrix of the lumped constant circuit is given by an expression:       F    T    =      [                                                      a              n                        ⁡                          (                              γ                ⁢                                  xe2x80x83                                ⁢                l                            )                                                                          Z              0                        ⁢                                          c                n                            ⁡                              (                                  γ                  ⁢                                      xe2x80x83                                    ⁢                  l                                )                                                                                                    1                              Z                0                                      ⁢                          xe2x80x83                        ⁢                                          b                n                            ⁡                              (                                  γ                  ⁢                                      xe2x80x83                                    ⁢                  l                                )                                                                                        a              n                        ⁡                          (                              γ                ⁢                                  xe2x80x83                                ⁢                l                            )                                            ]  
xe2x80x83where Z0 is a characteristic impedance of the distributed constant line.
d) Input of the error tolerance xcex5 is received and stored;
and the received xcex5 is used in the condition to decide the value of the n.
e) As the error tolerance xcex5, a plurality of values are received and stored;
and each value of the received xcex5 is used in the condition to decide the value of the n corresponding thereto.
Further, a second mode of the present invention provides a method of approximating a distributed constant line, which employs an information processing apparatus to perform a process of approximating an object distributed constant line by a lumped constant circuit obtained by cascading a given unit lumped constant circuit in n stages, comprising the steps of:
receiving input of a value of the n, and storing the value;
calculating a product xcex3l of a propagation constant xcex3 of the object distributed constant line and a line length l of the distributed constant line, and storing the product;
calculating cosh xcex3l and sinh xcex3l, using the xcex3l, and storing the cosh xcex3l and sinh xcex3l;
calculating an(xcex3l), bn(xcex3l) and cn(xcex3l) that constitute elements of a transfer matrix of the lumped constant line, from functions an(x), bn(x) and cn(x) defined by following three expressions:                     a        n            ⁢              (        x        )              =                  ∑                  k          =          0                n            ⁢                                                                  (                                  n                  +                  k                  -                  1                                )                            !                        ⁢                          xe2x80x83                                                                          n                                                      2                    ⁢                    k                                    -                  1                                            ⁢                              (                                  n                  -                  k                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                          2              ⁢              k                                                          (                              2                ⁢                k                            )                        !                                                  b        n            ⁢              (        x        )              =                  ∑                  k          =          0                          n          -          1                    ⁢                                                  (                              n                +                k                            )                        !                                                              n                                                      2                    ⁢                    k                                    +                  1                                            ⁢                              (                                  n                  -                  k                  -                  1                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                                          2                ⁢                k                            +              1                                                          (                                                2                  ⁢                  k                                +                1                            )                        !                                                  c        n            ⁢              (        x        )              =                  ∑                  k          =          0                n            ⁢                                                  (                                                n                  2                                +                                  k                  2                                            )                        ⁢                                          (                                  n                  +                  k                  -                  1                                )                            !                                                                          n                                                      2                    ⁢                    k                                    +                  1                                            ⁢                              (                                  n                  -                  k                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                                          2                ⁢                k                            +              1                                                          (                                                2                  ⁢                  k                                +                1                            )                        !                              
xe2x80x83putting x=xcex3l and deciding n as the value inputted, and storing the an(xcex3l), bn(xcex3l) and cn(xcex3l); and
calculating a deviation between the cosh xcex3l and an(xcex3l), a deviation between sinh xcex3l and bn(xcex3l), and a deviation between sinh xcex3l and cn(xcex3l), respectively, obtaining the maximum xcex4 among those deviations, and outputting the maximum xcex4 as an error.
A third mode of the present invention provides a system for approximating an object distributed constant line by a lumped constant circuit, comprising:
means for storing object circuit information describing the distributed constant line as an object of approximation, and approximate circuit information defining a lumped constant circuit obtained by cascading a given unit lumped constant circuit in n stages;
means for calculating a product xcex3l of a propagation constant xcex3 of the object distributed constant line and a line length l of the distributed constant line based on the object circuit information;
means for calculating cosh xcex3l and sinh xcex3l using the xcex3l;
means for calculating each of an(xcex3l), bn(xcex3l) and cn(xcex3l) that constitute elements of a transfer matrix of the lumped constant line, from functions an(x), bn(x) and cn(x) defined by following three expressions:                     a        n            ⁢              (        x        )              =                  ∑                  k          =          0                n            ⁢                                                                  (                                  n                  +                  k                  -                  1                                )                            !                        ⁢                          xe2x80x83                                                                          n                                                      2                    ⁢                    k                                    -                  1                                            ⁢                              (                                  n                  -                  k                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                          2              ⁢              k                                                          (                              2                ⁢                k                            )                        !                                                  b        n            ⁢              (        x        )              =                  ∑                  k          =          0                          n          -          1                    ⁢                                                  (                              n                +                k                            )                        !                                                              n                                                      2                    ⁢                    k                                    +                  1                                            ⁢                              (                                  n                  -                  k                  -                  1                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                                          2                ⁢                k                            +              1                                                          (                                                2                  ⁢                  k                                +                1                            )                        !                                                  c        n            ⁢              (        x        )              =                  ∑                  k          =          0                n            ⁢                                                  (                                                n                  2                                +                                  k                  2                                            )                        ⁢                                          (                                  n                  +                  k                  -                  1                                )                            !                                                                          n                                                      2                    ⁢                    k                                    +                  1                                            ⁢                              (                                  n                  -                  k                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                                          2                ⁢                k                            +              1                                                          (                                                2                  ⁢                  k                                +                1                            )                        !                              
xe2x80x83putting x=xcex3l and deciding n as a tentative value;
means for deciding the n by comparing the cosh xcex3l with an(xcex3l), sinh xcex3l with bn(xcex3l), and sinh xcex3l with cn(xcex3l), respectively, to make a judgment on whether a result of comparison satisfies a predetermined condition, and, when the condition is not satisfied, by repeating processes from a process of calculating the an(xcex3l), bn(xcex3l) and cn(xcex3l), onward, changing the value of the n, until the result of comparison satisfies the condition; and
means for deciding an approximate circuit, the means using n when the result of comparison satisfies the condition, in order to decide, as the approximate circuit, a lumped constant circuit that is obtained by cascading the unit lumped constant circuit in n stages.
In the above-mentioned system, further, the following modes may be optionally employed.
f) The above-mentioned means for deciding n:
carries out the comparison by calculating a deviation between the cosh xcex3l and an(xcex3l), a deviation between sinh xcex3l and bn(xcex3l), and a deviation between sinh xcex3l and cn(xcex3l), respectively, to obtain the result of comparison as the maximum xcex4 among those deviations; and
makes the judgment by using a condition that the maximum xcex4 and an error tolerance xcex5 set in advance satisfy xcex4 less than xcex5, as the condition.
g) The above-mentioned system further comprises means for receiving designation from outside;
the means for storing possesses approximate circuit information on a lumped constant circuit constituted by cascading a Π circuit as the unit lumped constant circuit in n stages, and approximate circuit information on a lumped constant circuit constituted by cascading a T circuit as the unit lumped constant circuit in n stages;
the means for calculating an(xcex3l), bn(xcex3l) and cn(xcex3l) calculates an(xcex3l), bn(xcex3l) and cn(xcex3l) concerning the lumped constant circuit constituted by cascading, in n stages, the unit lumped constant circuit that is designated through the means for receiving designation between the Π circuit and T circuit; and
the means for deciding the approximate circuit decides, as the approximate circuit, the lumped constant circuit constituted by cascading the designated unit lumped constant circuit in n stages.
Further, a fourth mode of the present invention provides a system for approximating an object distributed constant line by a lumped constant circuit, wherein,
the system comprises:
a storage device for storing a program and data; and
a central processing unit for executing the program to perform the approximation;
the storage device stores object circuit information describing the distributed constant line as an object of approximation, and approximate circuit information defining a lumped constant circuit obtained by cascading a given unit lumped constant circuit in n stages; and
the central processing unit carries out processes of:
calculating a product xcex3l of a propagation constant xcex3 of the object distributed constant line and a line length l of the distributed constant line based on the object circuit information;
calculating cosh xcex3l and sinh xcex3l using the xcex3l;
calculating each of an(xcex3l), bn(xcex3l) and cn(xcex3l) that constitute elements of a transfer matrix of the lumped constant line, from functions an(x), bn(x) and cn(x) defined by following three expressions:                     a        n            ⁢              (        x        )              =                  ∑                  k          =          0                n            ⁢                                                                  (                                  n                  +                  k                  -                  1                                )                            !                        ⁢                          xe2x80x83                                                                          n                                                      2                    ⁢                    k                                    -                  1                                            ⁢                              (                                  n                  -                  k                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                          2              ⁢              k                                                          (                              2                ⁢                k                            )                        !                                                  b        n            ⁢              (        x        )              =                  ∑                  k          =          0                          n          -          1                    ⁢                                                  (                              n                +                k                            )                        !                                                              n                                                      2                    ⁢                    k                                    +                  1                                            ⁢                              (                                  n                  -                  k                  -                  1                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                                          2                ⁢                k                            +              1                                                          (                                                2                  ⁢                  k                                +                1                            )                        !                                                  c        n            ⁢              (        x        )              =                  ∑                  k          =          0                n            ⁢                                                  (                                                n                  2                                +                                  k                  2                                            )                        ⁢                                          (                                  n                  +                  k                  -                  1                                )                            !                                                                          n                                                      2                    ⁢                    k                                    +                  1                                            ⁢                              (                                  n                  -                  k                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                                          2                ⁢                k                            +              1                                                          (                                                2                  ⁢                  k                                +                1                            )                        !                              
xe2x80x83putting x=xcex3l and deciding n as a tentative value;
deciding the n by comparing the cosh xcex3l with an(xcex3l), sinh xcex3l with bn(xcex3l), and sinh xcex3l with cn(xcex3l), respectively, to make a judgment on whether a result of comparison satisfies a predetermined condition, and, when the condition is not satisfied, by repeating the processes from the process of calculating the an(xcex3l), bn(xcex3l) and cn(xcex3l), onward, changing the value of the n, until the result of comparison satisfies the condition; and
deciding an approximate circuit, using n when the result of comparison satisfies the condition, in order to decide, as the approximate circuit, a lumped constant circuit that is obtained by cascading the unit lumped constant circuit in n stages.
Further, a fifth mode of the present invention provides a program recorded medium in which a program for making an information processing apparatus execute a process of approximating an object distributed constant line by a lumped constant circuit obtained by cascading a given unit lumped constant circuit in n stages is recorded, wherein:
the program makes the information processing apparatus execute processes of:
calculating a product xcex3l of a propagation constant xcex3 of the object distributed constant line and a line length l of the distributed constant line based on the object circuit information;
calculating cosh xcex3l and sinh xcex3l using the xcex3l;
calculating each of an(xcex3l), bn(xcex3l) and cn(xcex3l) that constitute elements of a transfer matrix of the lumped constant line, from functions an(x), bn(x) and cn(x) defined by following three expressions:                     a        n            ⁢              (        x        )              =                  ∑                  k          =          0                n            ⁢                                                                  (                                  n                  +                  k                  -                  1                                )                            !                        ⁢                          xe2x80x83                                                                          n                                                      2                    ⁢                    k                                    -                  1                                            ⁢                              (                                  n                  -                  k                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                          2              ⁢              k                                                          (                              2                ⁢                k                            )                        !                                                  b        n            ⁢              (        x        )              =                  ∑                  k          =          0                          n          -          1                    ⁢                                                  (                              n                +                k                            )                        !                                                              n                                                      2                    ⁢                    k                                    +                  1                                            ⁢                              (                                  n                  -                  k                  -                  1                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                                          2                ⁢                k                            +              1                                                          (                                                2                  ⁢                  k                                +                1                            )                        !                                                  c        n            ⁢              (        x        )              =                  ∑                  k          =          0                n            ⁢                                                  (                                                n                  2                                +                                  k                  2                                            )                        ⁢                                          (                                  n                  +                  k                  -                  1                                )                            !                                                                          n                                                      2                    ⁢                    k                                    +                  1                                            ⁢                              (                                  n                  -                  k                                )                                      !                          ⁢                  xe2x80x83                ⁢                              x                                          2                ⁢                k                            +              1                                                          (                                                2                  ⁢                  k                                +                1                            )                        !                              
xe2x80x83putting x=xcex3l and deciding n as a tentative value;
deciding the n by comparing the cosh xcex3l with an(xcex3l), sinh xcex3l with bn(xcex3l), and sinh xcex3l with cn(xcex3l), respectively, to make a judgment on whether a result of comparison satisfies a predetermined condition, and, when the condition is not satisfied, by repeating the processes from the process of calculating the an(xcex3l), bn(xcex3l) and cn(xcex3l), onward, changing the value of the n, until the result of comparison satisfies the condition; and
deciding an approximate circuit, using n when the result of comparison satisfies the condition, in order to decide, as the approximate circuit, a lumped constant circuit obtained by cascading the unit lumped constant circuit in n stages.
Further, a sixth mode of the present invention provides a program for making an information processing apparatus execute line by a lumped constant circuit obtained by cascading a given unit lumped constant circuit n stages, wherein:
the program makes the information processing apparatus execute processes of:
calculating a product xcex3l of a propagation constant xcex3 of the object distributed constant line and a line length l of the distributed constant line based on the object circuit information describing the object distributed constant line;
calculating cosh xcex3l and sinh xcex3l using the xcex3l;
calculating each of an(xcex3l), bn(xcex3l) and cn(xcex3l) that constitute elements of a transfer matrix of the lumped constant line, for functions an("khgr"), bn("khgr") and cn("khgr") defined by the following three expressions:                                           a            n                    ⁡                      (            χ            )                          =                              ∑                          k              =              0                        n                    ⁢                                                                      (                                      n                    +                    k                    -                    1                                    )                                !                                                                                  n                                                                  2                        ⁢                        k                                            -                      1                                                        ⁡                                      (                                          n                      -                      k                                        )                                                  !                                      ⁢                          xe2x80x83                        ⁢                                          χ                                  2                  ⁢                  k                                                                              (                                      2                    ⁢                    k                                    )                                !                                                                                                  b            n                    ⁡                      (            χ            )                          =                              ∑                          k              =              0                                      n              -              1                                ⁢                                                                      (                                      n                    +                    k                                    )                                !                                                                                  n                                                                  2                        ⁢                        k                                            +                      1                                                        ⁡                                      (                                          n                      -                      k                      -                      1                                        )                                                  !                                      ⁢                          xe2x80x83                        ⁢                                          χ                                                      2                    ⁢                    k                                    +                  1                                                                              (                                                            2                      ⁢                      k                                        +                    1                                    )                                !                                                                                                  c            n                    ⁡                      (            χ            )                          =                              ∑                          k              =              0                        n                    ⁢                                                                      (                                                            n                      2                                        +                                          k                      2                                                        )                                ⁢                                                      (                                          n                      +                      k                      -                      1                                        )                                    !                                                            n                                                      2                    ⁢                    k                                    +                                      1                    ⁢                                                                  (                                                  n                          -                          k                                                )                                            !                                                                                            ⁢                          xe2x80x83                        ⁢                                          χ                                                      2                    ⁢                    k                                    +                  1                                                                              (                                      2                    ⁢                    k                    ⁢                                          xe2x80x83                                        ⁢                    1                                    )                                !                                                        
xe2x80x83putting "khgr"=xcex3l and deciding n as a tenative value;
deciding the n by comparing the cosh xcex3l with an(xcex3l), sinh xcex3l with bn(xcex3l), and sinh (xcex3l), respectively, to make a judgement on whether a result of comparison staisfies a predetermined condition, and, wherein the condition is not satisfied, by repeating the processes from the process of calculating the an(xcex3l), bn(xcex3l) and cn(xcex3l), onward, changing the value of the n, until the result of comparison satisfies the condition; and
deciding an approximate circuit, using n when the result of comparison satisfies the condition, in order to decide, as the approximate circuit, the lumped constant circuit that is obtained by cascading the unit lumped constant circuit in n stages.
Here, for example, the program makes the comparison carried out by calculating a deviation between the cosh xcex3l and an(xcex3l), a deviation between sinh xcex3l and bn(xcex3l), and a deviation between sinh xcex3l and cn(xcex3l), respectively, to obtain the result of comparison as the maximum xcex4 among those deviations; and makes the judgment carried out by using a condition that the maximum xcex4 and an error tolerance xcex5 set in advance satisfy xcex4 less than xcex5, as the condition.
According to the present invention, a circuit board including a wiring system to be treated as a distributed constant line can be approximated as a whole by a lumped constant circuit. In addition, in approximating a distributed constant line by a lumped constant circuit, the approximation can be carried out with required accuracy. Thus, there is such effect that the accuracy of the analysis becomes clear. Further, it is possible to know the accuracy with which the approximation is carried out.